We can solve this question using matching operations (my favorite Quantitative Comparison strategy)

Key property: \((\sqrt{x})(\sqrt{y}) = \sqrt{xy}\)

Given:
Quantity A: \(\frac{\sqrt{yx} \sqrt{x} }{\sqrt{y}}\)

Quantity B: \(\frac{\sqrt{z}}{\sqrt{x^{-2}z}}\)


Multiply both quantities by \(\sqrt{y}\) to get:

Quantity A: \((\sqrt{yx})(\sqrt{x})\)

Quantity B: \(\frac{(\sqrt{z})(\sqrt{y})}{\sqrt{x^{-2}z}}\)


Multiply both quantities by \(\sqrt{x^{-2}z}\) to get:

Quantity A: \((\sqrt{yx})(\sqrt{x})(\sqrt{x^{-2}z})\)
Quantity B: \((\sqrt{z})(\sqrt{y})\)

Apply the above property to get:
Quantity A: \(\sqrt{(yx)(x)(x^{-2}z)}\)
Quantity B: \(\sqrt{yz}\)

Simplify:
Quantity A: \(\sqrt{yz}\)
Quantity B: \(\sqrt{yz}\)

Answer: C


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